Playexch Id Kelly Criteria Guide for Betting on A Game

When you lay a bet at Playexch Id, you receive the other punter's stake as a payment if the outcome does not happen, but you must pay the punter at the agreed odds if the outcome does happen. As previously, let p represent your anticipated likelihood of the outcome occurring. In this situation, you will lose the bet if the outcome occurs, but you will win if it does not.

If you win, your account balance will be W0(1 + f*(1-c)), whereas if you lose, your account balance will be W0(1 – f*(d-1).

Ensuring Account Balance Protection and Liability Considerations

We must impose the following constraint on f: 0 f*(d-1) 1, or equivalently, 0 f 1/(d-1). This stops you from losing money that is more than your account balance. Consider this your financial constraint. This is in contrast to the budget constraint for supporting an outcome: 0 < f < 1. It's worth noting that with a low odd bet of 1.01 and a $100 account value, you may lay a wager of up to $10,000, which is more than your account balance. This is due to the fact that your total possible liability equals ($10,000) (1.01 - 1) = $100.

In comparison, the highest you could lay for this wager at high odds of 101.00 is $1, which is significantly less than your account balance of $100. We use rather than for the upper limit to prevent your account from being depleted.